cp's OEIS Frontend

A259201 Number of partitions of n into ten primes.

%I A259201 #38 Sep 08 2022 08:46:13
%S A259201 1,1,1,2,2,3,4,4,5,7,8,9,11,11,14,16,18,20,25,24,31,33,38,39,48,47,59,
%T A259201 59,69,69,87,80,102,98,118,114,143,131,168,154,191,179,227,200,261,
%U A259201 236,297,268,344,300,396,345,442,390,509,431,576,493,641,551,729
%N A259201 Number of partitions of n into ten primes.
%H A259201 Alois P. Heinz, <a href="/A259201/b259201.txt">Table of n, a(n) for n = 20..10000</a>
%H A259201 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A259201 a(n) = [x^n y^10] Product_{k>=1} 1/(1 - y*x^prime(k)). - _Ilya Gutkovskiy_, Apr 18 2019
%F A259201 a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} A010051(r) * A010051(q) * A010051(p) * A010051(o) * A010051(m) * A010051(l) * A010051(k) * A010051(j) * A010051(i) * A010051(n-i-j-k-l-m-o-p-q-r). - _Wesley Ivan Hurt_, Jul 13 2019
%e A259201 a(23) = 2 because there are 2 partitions of 23 into ten primes: [2,2,2,2,2,2,2,2,2,5] and [2,2,2,2,2,2,2,3,3,3].
%o A259201 (Magma) [#RestrictedPartitions(k,10,Set(PrimesUpTo(1000))):k in [20..80]] ; // _Marius A. Burtea_, Jul 13 2019
%Y A259201 Column k=10 of A117278.
%Y A259201 Number of partitions of n into r primes for r = 1-9: A010051, A061358, A068307, A259194, A259195, A259196, A259197, A259198, A259200.
%Y A259201 Cf. A000040, A010051.
%K A259201 nonn,easy
%O A259201 20,4
%A A259201 _Doug Bell_, Jun 20 2015